This paper describes a set of algorithms for the production of a certain class of architectural plans. Each plan is made up from rectangular rooms arranged within a simple rectangular overall plan shape. The effective upper limit on the number of component rectangles which may presently be...

This paper attempts to demónstrate the rules governing the packing of rectangles into a general rectangular perimeter. The properties of a diagram expressing the relationships between the exterior lines and the interior lines forming such packings are shown. A classification of different kinds...

A parametric shape grammar that generates the ground plans of Palladio's villas is developed as a definition of the Palladian style. The grammar is applied to generate the plan for the Villa Malcontenta.

Rotations and Lorentz transformations are compared geometrically and algebraically for two-, three-, and four-dimensional space and space-time. The close analogy between the two types of transformation is revealed by means of orthogonal and pseudo-orthogonal matrices, complex numbers and double...

Abstract. This paper demonstrates the one-to-one correspondence between trivalent 3-polytopes and fundamental architectural schemes. Enumeration results from the literature of combinatorics are given and are related to the problem of counting various classes of architectural plans and their...

This paper examines the problem of distortion which arises when a projection on a screen is viewed at an angle. A quantitative parameter -- the rate of variation of the viewing angle as function of the projection <nobr>angle -- is</nobr> defined and this is used to produce 'distortion surfaces' by means of a...

One often wishes to draw accurately a perspective picture which resembles almost identically one's free-hand sketch of an object. This goal can be attained by means of a very simple graphical method that supplies the location of the point of sight and determines its links with the other elements...

Four isomorphisms linking architectural problems to combinatorial mathematics answer four questions: How many ways can a given population be partitioned into a given schedule of groups? What is the most probable way that a given population will divide into a given number of groups? How many ways...

Overconstrained linkages, not satisfying the Kutzbach mobility criterion, are considered. A mathematical technique is presented for the derivation of overconstraint conditions. Although these are essentially geometrical, the model employs algebraic methods normally used for the displacement...